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fast fourier transform

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Occasional Contributor
Posts: 8

fast fourier transform

Hello all,
I have a problem with the computation of the IFFT (FFT ( x)) where x is a vector.

I made 2 tests:

test1 : 4096x1 vector , resulting
IFFT (FFT (x)) is fine.

test2 : 4000000x1 vector , resulting IFFT (FFT( x)) after about 50000 records began to be ko.

my code:

%let NN=%sysevalf(4096);

proc iml;

use temp.H_primo_test;

read all var {x} into N;

z=J(&NN,1,.);

z = fft(N);

f=J(&NN,1,.);

f= ifft(z/(&NN));

quit;

it appears that the increase in the number of records creates problems for the Fast Fourier Transform.

it's correct?

thank you!

SAS Super FREQ
Posts: 3,619

fast fourier transform

I don't know what you are seeing or what your data are, but here is a program that correctly computes the FFT and IFFT of a signal with 4,000,000 elements. As far as I can tell, the FFT is computing correctly on this large vector:

proc iml;

NN = 4000000;

t = T(do(-10,10, 20/(NN-1)));

y = sin(t) - 2*sin(2*t) + 3*sin(3*t) + 0.1*rannor(t);

z = fft(y);

f= ifft(z/NN);

maxdiff = max(abs(y-f));

print maxdiff;

maxdiff
5.5052E-9


It's possible that your data are causing instabilities of some sort. Check to see if they are blowing up (spanning many orders of magnitude) or are widely oscilating or are otherwise degenerate.

Occasional Contributor
Posts: 8

fast fourier transform

Thank you Rick.

Your maxdiff is E-9 depends on the elements of the input vector.

My vector is composed of very small values (E-3, E-6...) so the differences are consistent.

However, you confirm that SAS creates differences by calculating the IFFT(FFT))?

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